Issolvi 2{left(-sqrt{2}-1right)}^2-2

$$2 { \left(- \sqrt{ 2 } -1 \right) }^{ 2 } -2$$

Evalwa

$$4\left(\sqrt{2}+1\right)\approx 9.656854249$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(-\sqrt{2}-1\right)^{2}.

$$2\left(\left(-\sqrt{2}\right)^{2}-2\left(-\sqrt{2}\right)+1\right)-2$$

Ikkalkula -\sqrt{2} bil-power ta' 2 u tikseb \left(\sqrt{2}\right)^{2}.

$$2\left(\left(\sqrt{2}\right)^{2}-2\left(-\sqrt{2}\right)+1\right)-2$$

Immultiplika -2 u -1 biex tikseb 2.

$$2\left(\left(\sqrt{2}\right)^{2}+2\sqrt{2}+1\right)-2$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'\left(\sqrt{2}\right)^{2}+2\sqrt{2}+1.

$$2\left(\sqrt{2}\right)^{2}+4\sqrt{2}+2-2$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$2\times 2+4\sqrt{2}+2-2$$

Immultiplika 2 u 2 biex tikseb 4.

$$4+4\sqrt{2}+2-2$$

Żid 4 u 2 biex tikseb 6.

$$6+4\sqrt{2}-2$$

Naqqas 2 minn 6 biex tikseb 4.

$$4+4\sqrt{2}$$

Espandi

$$4 \sqrt{2} + 4 = 9.656854249$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(-\sqrt{2}-1\right)^{2}.

$$2\left(\left(-\sqrt{2}\right)^{2}-2\left(-\sqrt{2}\right)+1\right)-2$$

Ikkalkula -\sqrt{2} bil-power ta' 2 u tikseb \left(\sqrt{2}\right)^{2}.

$$2\left(\left(\sqrt{2}\right)^{2}-2\left(-\sqrt{2}\right)+1\right)-2$$

Immultiplika -2 u -1 biex tikseb 2.

$$2\left(\left(\sqrt{2}\right)^{2}+2\sqrt{2}+1\right)-2$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'\left(\sqrt{2}\right)^{2}+2\sqrt{2}+1.

$$2\left(\sqrt{2}\right)^{2}+4\sqrt{2}+2-2$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$2\times 2+4\sqrt{2}+2-2$$

Immultiplika 2 u 2 biex tikseb 4.

$$4+4\sqrt{2}+2-2$$

Żid 4 u 2 biex tikseb 6.

$$6+4\sqrt{2}-2$$

Naqqas 2 minn 6 biex tikseb 4.

$$4+4\sqrt{2}$$